In: Statistics and Probability
Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data.
Predictor | Coef | SE Coef | T | P |
Constant | -0.209 | 2.429 | -0.09 | 0.929 |
Diameter | 0.7554 | 0.1416 | 5.33 | 0.021 |
S = 4.05660 | R-Sq = 80.5% |
(a) The standard error Se of the linear
regression model is given in the printout as "S." What is the value
of Se?
(b) The standard error of the coefficient of the predictor variable
is found under "SE Coef." Recall that the standard error for
b is
Se/√Σx2 –
(1/n)(Σx)2. From the Minitab
display, what is the value of the standard error for the slope
b?
(c) The formula for the margin of error E for a
c% confidence interval for the slope β can be
written as E = tc(SE Coef). The Minitab display
is based on n = 16 data pairs. Find the critical value
tc for a 99% confidence interval in the
relevant table. Then find a 99% confidence interval for the
population slope β. (Use 3 decimal places.)
tc | |
lower limit | |
upper limit |